A warm August evening, 2009, and strange things are afoot in a converted church hall at the bottom of Edinburgh's historic Grassmarket. In some freak booking accident, BBQ obsessed Scandinavian free jazz berserkers The Thing are laying waste to the city's notoriously conservative Jazz and Blues Festival. Sweat dripping down his forehead, Mats Gustafsson grapples with his baritone saxophone, its monstrous valves belching out heavy riffs and high-pitched squalls. At his side, Ingebrit Håker Flaten wrestles with his double bass, exploring its percussive qualities as much as its harmonic range. Behind them, drummer Paal Nilssen-Love's arms are a blur, creating a whirlwind of polyrhythms as his bass drum pounds away in a metre of its own. Out of freewheeling improvisations emerge recognisable nuggets of rock riffage: Lightning Bolt, PJ Harvey, Black Sabbath's 'Iron Man'. It's riveting stuff, and far from inaccessible. It's by no means all balls to the wall skronk: there's an extreme dynamic range to their performance, as they work out the acoustics of the room and push their instrumental technique to the limits in search of new sounds.

It's tempting to associate The Thing with John Carpenter's shape-changing alien, a weird and pissed-off creature lurking in the icy hyperborean wastes. But in fact, they're named after a piece by jazz legend Don Cherry, from his brilliant 1966 album on Blue Note, Where Is Brooklyn? Originally conceived as a one-off project in tribute to Cherry – their self-titled debut is a caffeinated update of '60s free-bop - The Thing soon morphed into something strange and hairy. A spooked, wheezing version of PJ Harvey's 'To Bring You My Love', recorded with veteran free jazzer Joe McPhee in 2001, announced The Thing's affinity with alternative rock, an allegiance they would cement with 2005's Garage.

All too often, jazz acts get rock horribly wrong. As Frances Morgan writes, “cross-genre interpretation, if it is to work musically and not just as a point of interest, is about a connection that goes beyond the merely formal”. That's why piano trio the Bad Plus's version of 'Smells Like Teen Spirit' is a failure; it's kitsch, a collegiate exercise in novelty. They take the tune and the riff, but fail to harness the power of Nirvana's original. The Thing, however, are drawn to what Gustafsson has called “the energy parameter”. Great energy music, whatever the genre, transcends form to reach an ecstatic pitch. It pushes past meaning to take you beyond yourself. It's electrifying, sublime.

As Gustafsson told Morgan in 2009, “It doesn't mean it has to be loud, but we are attracted by music that has this resistance and tension”. The Thing use rock riffs as a basis for improvisation, mangling them into wild new shapes. Talking to The Quietus's Matt Evans, Gustafsson explained, “All the great music we can find, we try to use — be it hardcore or metal, tropicalia or schlager, noise or garage rock, free jazz or West Coast, we try to make it our music. The Thing’s music.”

The Thing's music, then, can be located within several jazz traditions: the fire music of Albert Ayler, the sparse atmospherics of Don Cherry's Mu, the full-blooded European improvisation of Peter Brotzmann, and the brutal “snuff-jazz” of no-wave trio Borbetomagus. But they also have allegiances with noise, avant-rock and punk. Gustafsson has played with Sonic Youth, The Ex and Zu, while Nilssen-Love and Håker Flaten make febrile out-rock with guitarist Raoul Bjorkenheim as Scorch Trio. Recently, The Thing have been playing with Neneh Cherry, a collaboration which makes perfect sense considering their debt to her stepfather. A live clip sees Cherry in captivating form, channeling MF Doom lyrics while the band keep it low key. There's something of the free-funk of Art Ensemble of Chicago circa Les Stances A Sophie to it, making an album a tantalising prospect.

A discography of all three members' projects would surely run into treble figures, and I cannot claim to be au fait with it all. As this article takes The Thing as its starting point, I've decided to leave out releases which pre-date that group's existence. If you can track it down, however, Gustafsson's 1995 duo exchange with the great Chicago drummer Hamid Drake, For Don Cherry, is a stunning showcase of the saxphonist's subtler side, with elegiac solos emerging from stretches of near silence. The following selection, then, is a personal selection of relatively recent transmissions from Planet Thing. There's some great music on limited or out of print releases, but in the interests of accessibility, I've favoured recordings which are readily available, many of them on Oslo's mighty Smalltown Superjazzz.

The Thing - Action Jazz (Smalltown Superjazzz, 2006)

Garage heralded The Thing's punk-jazz direction with a gleeful cover of the Yeah Yeah Yeah's 'Art Star' and an ugly lurch through the White Stripes's 'Aluminium'. Action Jazz tops it, however, with an inspired take on Lightning Bolt's 'Ride The Sky'. It begins as an act of riff worship, the trio united in devotion to that primordial stomp, before Gustafsson breaks loose, howling pterodactyls fleeing the arcs of hot lava sputtering from his horn. Ornette Coleman's 'Broken Shadows' finds the group in a small hours mood, and the great man's influence is all over the free-blues of 'The Nut/The Light', written, curiously enough, by Gustafsson's daughter Alva Melin of teenage punk duo Drap En Hund. More accessible than subsequent releases, Action Jazz finds a balance between the stoopid-fun of their garage material, the swing of their Cherry inspired free-bop, and the open-form weirdness to come.

In which our heroes hook up with Norwegian garage rockers Cato Salsa Experience and the legendary Joe McPhee to prove that sleazy Crampsian guitar riffs sound all the better when doubled with honking saxophones. This is easily the most 'rock' record The Thing have made, but by bringing free-blowing and primitive electronics to the party, they push the garage sound into places trad bores like Jet or The Datsuns could never imagine. A version of The Sonics' 'The Witch' begins with a bowed bass solo that evokes squeaky doors and vomitting goblins, before the whole band pile in with that immortal riff. An athletic climax sees Nilssen-Love take the tempo up to breakneck speed while McPhee unleashes a wailing tenor solo, underscored by flatulent honks from Gustafsson's baritone. James Blood Ulmer's 'Baby Talk' sees the guitars getting weird while the horns play the catchy melody, while Mongezi Feza's 'You Ain't Gonna Know Me 'Cos You Think You Know Me' offers a more reflective side to the group, with McPhee's wistful saxophone orbited by spacey slide guitar and theremin. If you enjoy McPhee's playing on this, check out his excellent 2007 album with Nilssen-Love, Tomorrow Came Today, or his classic Nation Time (1970), an astounding mix of fire music, JBs funk and black revolutionary chants.

The Thing - Bag It! (Smalltown Superjazzz, 2009)

Recorded by noted jazzophobe Steve Albini, Bag It! takes The Thing's improvisations further out, with electronics taking a much more prominent role. Cato Salsa Experience's 'Drop The Gun' begins in classic Garage style, before Gustafsson takes the title's advice and swaps his horn for a twin-input mixer, showering fuzzy static and swooping test tones over a thumping beat. Respect is paid to jazz history with covers of Duke Ellington's 'Mystery Song' and Albert and Don Ayler's 'Angels'. Doing justice to the liberated spirit of the Aylers' beautiful melody is no small task, but Gustafsson nails it, bringing a breathy grain to his tender tone. Nilsson-Love sensitively deploys metal on metal percussion effects, while alien radiophonics hover past. The second disc consists of a 30 minute live improvisation, 'Beef Brisket', where The Thing open up their full dynamic and timbral range. As the music reaches an ecstatic pitch, Gustafsson can be heard screaming down the mouthpiece of his horn, while Håker Flaten's overdriven bass roars like a revving engine. A long way from the garage romps of yore, Bag It! is undoubtedly the trio's finest achievement to date.

Two live dates from 2008-09, recorded with guitarists Yoshihide and O'Rourke at Tokyo experimental music hub Shinjuku Pitt Inn. There's no garage rock here; these sets are entirely improvised, testament to The Thing's willingness to challenge themselves through collaboration.

Gustafsson and O'Rourke have worked together regularly since their involvement in the Chicago experimental scene of the '90s, and the latter's fried guitar work helps make some of the rawest music The Thing have made. It begins quietly enough, with Nilsson-Love's hand bells and cymbal scrapes complimented by squelchy bass throbs and purring baritone sax. Then Gustafsson slowly comes to life, a yawning and slobbering komodo dragon. O'Rourke introduces needling fuzz guitar lines, and the whole thing kicks off. From a solid blues foundation, the rhythm section works itself into a frenzy, O'Rourke's screaming slide eruptions alternating with Gustafsson's wailing tenor.

As its title suggests, Shinjuku Crawl is a less of a blow-out, showing Japanese heavyweight Yoshihide's sensitive use of electric guitar noise, treating it as a textural element among acoustic instruments, and not an overbearing wall of fuzz. Nilssen-Love is on particularly impressive form, creating unusual percussive effects around Yoshihide's impressionistic smears of tone and Gustafsson's barely-there rasps. Rest assured, they still do go nuts, with Yoshihide scrabbling across the fretboard and working the wah-wah pedal like the bastard child of Hendrix and Derek Bailey while Nilssen-Love clatters away. Gustafsson gives them plenty of space in which to work, so that when his horn does come raging in, the results are a face-melting joy.

Zu vs Mats Gustafsson – How To Raise An Ox (Atavistic, 2005)

A dark, fetid descent into industrial horror, How To Raise An Ox sees Gustafsson and Zu become the house band in a Giallo slaughterhouse. Bassist Mario Pupillo's vicious flesh on metal grind and Jacopo Battaglia's powerhouse free-rock drumming is the twitching carcass from which Gustafsson and fellow sax fiend Luca Mai carve hideous shapes. When they go all out it's thrilling, but they're most effective when creating a dank, sinster atmosphere, such as in 'The King Devours His Sons', where Gustafsson's sax circles vulture-like over Pupillo's creeping bass. Gustafsson and Pupillo would meet again in the excellent improvising rock group Original Silence, alongside Nilsson-Love, Thurston Moore, Jim O'Rourke and Terrie Ex. Very different in mood from How To..., their two albums are a good-natured clash of musical personalities.

One of the strangest and quietest entries in the Gustafsson discography, this hook up with Yoshimi of the Boredoms and OOIOO is perhaps the most beautiful. That's not to say it's an easy listen, but the sustained mood of otherworldly devotion created by voice, electronics and reeds is quite magical. Yoshimi's vocals lead the improvisation, as she works over melodic phrases with throat, mouth and electronic manipulation. Gustafsson deploys a range of horns, from his regular tenor and baritone to the slide saxophone and plastic fluteophone. He's admirably restrained, laying modulating drones and puffing key taps under Yoshimi's gorgeous incantations, making his brief forays into overblown multiphonics all the more affecting. After 45 minutes, it falls away in wispy delay trails, leaving your mind adrift in the cosmos.

As the unholy father of European extreme-jazz, Peter Brotzmann has at times been unfairly dismissed as a macho noisenik. Even today, Brotz's monstrous lungs can summon incredible sonic power, but there is remarkable sensitivity and invention to his playing. He clearly sees something of himself in Gustafsson, who, along with Nilssen-Love, is a member of his sprawling Chicago Tentet. A 5-CD boxset of that group is available, but this live set seems a more appropriate selection here, with each player on an equal footing. Opener 'Bullets Through Rain' is ten minutes of barbaric yawp, Brotzmann's tenor a wild squall around Gustafsson's baritone blare. With no bassist involved, it's up to Nilsson-Love to bring the heavy, and he works the kick and floor tom hard, without losing that swing. The following two pieces are longer, exploratory pieces, ranging from nuanced lyricism to hair-raising din. The horns conjure a menagerie of flustered elephants, snoring bears, and storm-tossed gulls, while the drums rumble and crack. But there's also some downright beautiful playing, especially in the sax and bass clarinet exchange a few minutes into 'Colours In Action'.

Members of The Thing have a long-running association with Chicago reedsman Vandermark, who brings soulful tone and bop phrasing to an adventurous range of projects. For Lean Left, Vandermark and Nilsson-Love team up with Ex guitarists Terrie Hessels and Andy Moor, testament to the questing spirit of all parties. This set begins as melodic and energetic sax and drums duet, the guitarists only entering after ten minutes. Choppy punk chords gradually give way to scratchy trebles and fidgety improv twangs, but the energy levels rarely diminish. Nilssen-Love's stamina is astonishing, as he bumps and rolls behind the guitar clank and swoops and squawks of saxophone.

Gustafsson joined Akita, aka Japanese noise overlord Merzbow, and O'Rourke for Sonic Youth's SYR 8, one of their better recent jams. This studio date, however, strips out the rock or jazz to consider the possibilities of noise. There are painful sounds on here, but it's never the dense, unvarying assault some might associate with the idiom. Akita opens by laying a pure, high tone over a rinsing digital gush, while O'Rourke draws low hums and twinkling highs from a feedbacking amp. Gustafsson soon comes in, playing the same note over and over, building in intensity until it becomes a ragged foghorn. Akita sets off what sound likes a circular saw, its pitch wavering in and out of harmony with the horn. Technoid bass tones creep in, while Gustafsson howls like a dragon in a tarpit. Doomy synth tones collapse into irregular pulses, while metal is dragged across a dungeon floor. A stomping bass drum stalks the blasted landscape, while Gustafsson slaps his tongue around the mouthpiece like a predator eyeing up his quarry. If the first side is about low-end dread, the second is about harsher high frequencies, with rain on tin distortion, slashes of feedback and squealing sax.

Fire! Trio + Jim O'Rourke – Untitled? (Rune Gramafon, 2011)

Fire! Trio is a relatively controlled affair, more hypnodelic rock than free jazz. Gustafsson, bassist Johan Berthling (Tape) and drummer Andreas Werling (Wildbirds & Peacedrums), are joined by Jim O'Rourke for this second album. 'Happy Ending Borrowing Yours' is the climax of this trip, a slow-burning bass throb which uncoils to release a primordial baritone sax solo from Gustafsson, O'Rourke sneaking up from behind with mangled guitar and frazzled electronics. Werling is on point throughout, his deceptively simple drumming the foundation of this elemental music.

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